Geodesic
A method for shock calculation
Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 60-70.

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The mass, momentum and energy conservation laws allow shock and rarefaction waves to be present in the solution of continuum mechanics problems. When these problems are solved with homogeneous difference techniques, the strong shock surface is represented by a layer of a finite width within which the quantities vary continuously from a state before the shock front to a state behind it. These states are related by the strong shock conditions. Since they lie on the Hugoniot, there must exist a mechanism which maintains energy dissipation in the shock layer. One of these mechanisms is a method by Kuropatenko which uses the difference equations applicable for strong shocks. The method can be implemented in different difference schemes. The paper presents one of them, describes its basic properties, and provides results of some calculations.
Mots-clés : conservation laws, energy dissipation, difference scheme, shock, rarefaction. 
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V. F. Kuropatenko; M. N. Yakimova. A method for shock calculation. Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 60-70. https://geodesic-test.mathdoc.fr/item/JCEM_2015_2_2_a5/

[1] B. L. Rozhdestvensky, N. N. Yanenko, Systems of Quasi-linear Equations and Their Applications in Hydrodynamics, Nayka Publ., Moscow, 1968

[2] V. F. Kuropatenko, “On Difference Methods for Hydrodynamic Equations”, Trudy Matem. Instituta im. V.A. Steklova ANSSSR – Works MIAN, 74:1 (1966), 107–137 | MR | Zbl

[3] V. F. Kuropatenko, I. R. Makeeva, “Study of Discontinuity Distraction for Methods of Shock Wave Calculations”, Matem. Mod., 18:3 (2006), 120–128 | MR | Zbl

[4] J. Neumann, R. Richtmayer, “A Method for the Numerical Calculation of Hydrodynamical Shocks”, J. Appl. Phys, 21:3 (1950), 232–237 | DOI | MR | Zbl

[5] P. D. Lax, “Weak Solution of Nonlinear Hyperbolic Equations and Their Numerical Computations”, Comn. Pure and Appl. Math, 7 (1954), 159–193 | DOI | MR | Zbl

[6] S. K. Godunov, “Difference Method of Computation of Shock Waves”, Uspekhi Mat. Nauk, 12:1(73) (1957), 176–177 | MR | Zbl

[7] V. F. Kuropatenko, “A Shock Calculation Method”, DAN SSSR, 3:4 (1960), 771–772 | MR

[8] V. F. Kuropatenko, “Lokalnaya konservativnost raznostnykh skhem dlya uravnenii gazovoi dinamiki”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 25:8 (1985), 1176–1188 | MR

[9] V. F. Kuropatenko, I. A. Dorovskikh, I. R. Makeyeva, “The Effects of Difference Schemes Properties on the Mathematical Simulation of Dynamic Processes”, Computational Technology, 11:2 (2006), 3–12 | Zbl

[10] V. F. Kuropatenko, G. V. Kovalenko, V. I. Kuznetsova, G. I. Mikhaylova, “Code and Inhomogeneous Difference Method for Simulating Non-Equilibrium Compressible Continuum Flows”, Problems in Nuclear Science and Engineering Journal, Series: Mathematical Modeling of Physical Processes, 1989, no. 2, 9–17